Say it again: umlaut! It's just a fun word to say. However, the umlaut leads to some of the most difficult pronunciations in German, to the frustration of many a student of German.
The umlaut only appears over vowels, and at that, only over ä, ö, and ü. The sound it makes is difficult for English speakers to imitate: In standard German, it is as if you are about to add an r sound to the vowel and shape your mouth to do so, but don't actually make the r sound, going instead going on to the next sound.
Umlauted vowels can be transcribed into more basic letters, as ae, oe and ue, respectively—just by adding an e to the end. Most Germans look down on using this, only making use of it when the umlaut is absolutely unavailable on a keyboard. By no means are they considered the proper spelling.
While most German dialects, including standard German, simply capitalize umlauted vowels by capitalizing the underlying vowel and then adding the umlaut as usual over the top, some dialects, including Swiss German, capitalize umlauted vowels by rendering it in its transcribed state and then capitalizing the first of the two vowels, e.g. Ae instead of Ä.
As you might guess, words beginning with umlauted vowels might cause some confusion in dictionaries, indexes and other alphabetically sorted texts. Sometimes they are sorted as if they were just normal letters (e.g. ax,äy, az), sometimes as if they were in their transcribed state (e.g. ad, ä (ae), af), sometimes just taking second priority to the unumlauted vowels (e.g. anb, änb, anb or an, anb, än.) Be prepared to look under multiple headings if you don't immediately find what you're looking for!
Here's an interesting phenomenon: Many brand names borrow the umlaut for the purpose of mere decoration or making it appear more foreign while having no actual impact on the pronunciation. A popular example is the Häagen-Dazs brand of tasty tasty ice cream.